Finite Group Databasebeta

← #29589537

Subgroups — #29589537

Order 15616.

492 conjugacy classes of subgroups; only the 83 normal subgroups are shown.

normal subgroups only

This group has 492 conjugacy classes of subgroups — too many to draw. Only its 83 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21450097C211yesmaximal, characteristic
2#21444146C211yesmaximal, characteristic
3#21443768C212yesmaximal, complemented
4#21443748C212yesmaximal, complemented
5C2×C61×#323C211yesmaximal, characteristic
6C22×C22⋊Dic61C411yescharacteristic
7#16839726—21no—
8#16839690—21no—
9#16839690—21no—
10#16839635—21no—
11#16839634C411yescharacteristic
12#16839634C2211yescharacteristic
13#16839625—21no—
14#16839623C411yescharacteristic
15#16839623C2211yescharacteristic
16#16839618C411yescharacteristic
17#16839486—21no—
18#16839486C2212yes—
19C22×C22⋊C4×C61C2211yescharacteristic
20C2×C22⋊C8×C61—21no—
21C61×#323—21no—
22C61×#323C2212yes—
23C23×Dic61C2×C411yescharacteristic
24C23×Dic61C2×C411yescharacteristic
25C2×#11758194—41no—
26C2×#11758196—21no—
27C2×#11758196—21no—
28C2×C22⋊Dic61—21no—
29C2×C22⋊Dic61—21no—
30C2×C22⋊Dic61—21no—
31C2×C22⋊Dic61—21no—
32C2×C22⋊Dic61—41no—
33C2×C22⋊Dic61—41no—
34C2×C22⋊Dic61C2×C411yescharacteristic
35C2×C22⋊Dic61C2×C411yescharacteristic
36C22⋊#92418—22no—
37C22⋊#92418—41no—
38#14519684—21no—
39#14519684—21no—
40#14519684—21no—
41#14519684—21no—
42#14519684—21no—
43#14519684—21no—
44C25×C61C2×C411yescharacteristic
45C23×C4×C61D411yescharacteristic
46C23×C4×C61D411yescharacteristic
47C22×C8×C61—41no—
48C2×C22⋊C4×C61—41no—
49C2×C22⋊C4×C61—41no—
50C2×C22⋊C4×C61C2×C411yescharacteristic
51C2×C22⋊C4×C61D411yescharacteristic
52C2×C22⋊C4×C61D411yescharacteristic
53C2×C22⋊C4×C61C2311yescharacteristic
54C22⋊C8×C61—22no—
55C22⋊C8×C61—41no—
56C24×C61—21no—
57C24×C61—21no—
58C24×C61—22no—
59C24×C61—41no—
60C24×C61—42no—
61C24×C61—81no—
62C24×C61C22⋊C411yescharacteristic
63C24×C61C22⋊C411yescharacteristic
64C24×C61C22×C411yescharacteristic
65C22×C4×C61—21no—
66C22×C4×C61—21no—
67C22×C4×C61—21no—
68C22×C4×C61—21no—
69C22×C4×C61—42no—
70C22×C4×C61—81no—
71C22×C4×C61C22⋊C411yescharacteristic
72C22×C4×C61C22⋊C411yescharacteristic
73C22×C4×C61C2×D411yescharacteristic
74C22×C4×C61C2×D411yescharacteristic
75C22×Dic61—21no—
76C22×Dic61—21no—
77C22×Dic61—21no—
78C22×Dic61—21no—
79C22×Dic61—22no—
80C22×Dic61—41no—
81C22×Dic61—41no—
82C22×Dic61—41no—
83C22×Dic61—81no—
84C2×C8×C61—42no—
85C2×C8×C61—82no—
86C22⋊C4×C61—41no—
87C22⋊C4×C61—41no—
88C22⋊C4×C61—41no—
89C22⋊C4×C61—41no—
90C22⋊Dic61—22no—
91C22⋊Dic61—42no—
92C22⋊Dic61—42no—
93C22⋊Dic61—41no—
94C22⋊Dic61—41no—
95C22⋊Dic61—41no—
96C22⋊Dic61—81no—
97#11758196—81no—
98#11758196—81no—
99#11758194—82no—
100C2×#92418—42no—
101C23×C61—22no—
102C23×C61—21no—
103C23×C61—21no—
104C23×C61—21no—
105C23×C61—21no—
106C23×C61—21no—
107C23×C61—21no—
108C23×C61—21no—
109C23×C61—41no—
110C23×C61—42no—
111C23×C61—42no—
112C23×C61—41no—
113C23×C61—41no—
114C23×C61—42no—
115C23×C61—41no—
116C23×C61—41no—
117C23×C61—42no—
118C23×C61—81no—
119C23×C61—81no—
120C23×C61—84no—
121C23×C61—84no—
122C23×C61#9911yescharacteristic
123C23×C61#9911yescharacteristic
124C23×C61C2×C22⋊C411yescharacteristic
125C23×C61#13112yes—
126C2×C4×C61—21no—
127C2×C4×C61—21no—
128C2×C4×C61—21no—
129C2×C4×C61—21no—
130C2×C4×C61—42no—
131C2×C4×C61—42no—
132C2×C4×C61—41no—
133C2×C4×C61—41no—
134C2×C4×C61—41no—
135C2×C4×C61—41no—
136C2×C4×C61—81no—
137C2×C4×C61—81no—
138C2×Dic61—41no—
139C2×Dic61—41no—
140C2×Dic61—41no—
141C2×Dic61—41no—
142C2×Dic61—41no—
143C2×Dic61—41no—
144C2×Dic61—41no—
145C2×Dic61—41no—
146C2×Dic61—41no—
147C2×Dic61—41no—
148C2×Dic61—41no—
149C2×Dic61—41no—
150C2×Dic61—82no—
151C2×Dic61—82no—
152C8×C61—82no—
153#92418—82no—
154#11543—611nomaximal, Sylow
155C22×C61—21no—
156C22×C61—21no—
157C22×C61—21no—
158C22×C61—21no—
159C22×C61—21no—
160C22×C61—21no—
161C22×C61—22no—
162C22×C61—21no—
163C22×C61—42no—
164C22×C61—42no—
165C22×C61—42no—
166C22×C61—42no—
167C22×C61—41no—
168C22×C61—41no—
169C22×C61—41no—
170C22×C61—41no—
171C22×C61—41no—
172C22×C61—84no—
173C22×C61—81no—
174C22×C61—81no—
175C22×C61—84no—
176C22×C61#35212yes—
177C22×C61#40811yescharacteristic
178C22×C61C2×#9911yescharacteristic
179C22×C61#41311yescharacteristic
180C4×C61—41no—
181C4×C61—41no—
182C4×C61—41no—
183C4×C61—41no—
184Dic61—81no—
185Dic61—81no—
186Dic61—81no—
187Dic61—81no—
188#2483—611no—
189#1462—611no—
190C2×#323D6111yescharacteristic
191#1326—612no—
192#1317—612no—
193C2×C61—21no—
194C2×C61—21no—
195C2×C61—22no—
196C2×C61—41no—
197C2×C61—42no—
198C2×C61—81no—
199C2×C61#146811yescharacteristic
200C2×C61C2×#35211yescharacteristic
201C2×C61#212111yescharacteristic
202C22×C22⋊C4—611no—
203C22×C22⋊C4C2×D6111yescharacteristic
204#407—1221no—
205C2×C22⋊C8—21no—
206#397—1221no—
207#397—1221no—
208#385—611no—
209#385—611no—
210#385—1221no—
211#381—611no—
212#381—611no—
213#381—1221no—
214#379—611no—
215#323—21no—
216#323—612no—
217#323—1221no—
218#323C2×D6112yes—
219C61#1154311yescharacteristic, complemented, Sylow
220C25C4×D6111yescharacteristic
221C23×C4—611no—
222C23×C4—611no—
223C23×C4D24411yescharacteristic
224C23×C4C22⋊D6111yescharacteristic
225C2×M16—2441no—
226C22×C8—41no—
227C2×C4⋊C4—1221no—
228C2×C4⋊C4—1221no—
229C2×C22⋊C4—41no—
230C2×C22⋊C4—41no—
231C2×C22⋊C4—611no—
232C2×C22⋊C4—611no—
233C2×C22⋊C4—1221no—
234C2×C22⋊C4—1221no—
235C2×C22⋊C4—1221no—
236C2×C22⋊C4—1221no—
237C2×C22⋊C4—2441no—
238C2×C22⋊C4—2441no—
239C2×C22⋊C4C4×D6111yescharacteristic
240C2×C22⋊C4D24411yescharacteristic
241C2×C22⋊C4C22⋊D6111yescharacteristic
242C2×C22⋊C4C22×D6111yescharacteristic
243C22⋊C8—22no—
244C22⋊C8—41no—
245C22⋊C8—1222no—
246C22⋊C8—2441no—
247#95—1221no—
248#95—1221no—
249#95—1221no—
250#95—1221no—
251#95—1221no—
252#95—1221no—
253C24—21no—
254C24—21no—
255C24—22no—
256C24—41no—
257C24—42no—
258C24—81no—
259C24#1175819811yescharacteristic
260C24#1175819811yescharacteristic
261C24C2×C4×D6111yescharacteristic
262C22×C4—21no—
263C22×C4—21no—
264C22×C4—21no—
265C22×C4—21no—
266C22×C4—42no—
267C22×C4—81no—
268C22×C4—1222no—
269C22×C4—1221no—
270C22×C4—1221no—
271C22×C4—1221no—
272C22×C4—1221no—
273C22×C4—4881no—
274C22×C4—2441no—
275C22×C4—2441no—
276C22×C4—2441no—
277C22×C4#1175819811yescharacteristic
278C22×C4#1175819811yescharacteristic
279C22×C4C2×D24411yescharacteristic
280C22×C4C2×C22⋊D6111yescharacteristic
281M16—4882no—
282C2×C8—42no—
283C2×C8—82no—
284C2×C8—2442no—
285C4⋊C4—4881no—
286C4⋊C4—4881no—
287C22⋊C4—41no—
288C22⋊C4—41no—
289C22⋊C4—41no—
290C22⋊C4—41no—
291C22⋊C4—1222no—
292C22⋊C4—4881no—
293C22⋊C4—2442no—
294C22⋊C4—2442no—
295C22⋊C4—2441no—
296C22⋊C4—2441no—
297C22⋊C4—2441no—
298C23—21no—
299C23—21no—
300C23—21no—
301C23—21no—
302C23—22no—
303C23—21no—
304C23—21no—
305C23—21no—
306C23—41no—
307C23—42no—
308C23—42no—
309C23—41no—
310C23—41no—
311C23—42no—
312C23—41no—
313C23—41no—
314C23—42no—
315C23—81no—
316C23—81no—
317C23—84no—
318C23—84no—
319C23#1451969111yescharacteristic
320C23#1451969111yescharacteristic
321C23C2×#1175819811yescharacteristic
322C23#1451978312yes—
323C2×C4—21no—
324C2×C4—21no—
325C2×C4—21no—
326C2×C4—21no—
327C2×C4—42no—
328C2×C4—42no—
329C2×C4—41no—
330C2×C4—41no—
331C2×C4—41no—
332C2×C4—41no—
333C2×C4—81no—
334C2×C4—81no—
335C2×C4—4882no—
336C2×C4—4882no—
337C2×C4—2441no—
338C2×C4—2441no—
339C2×C4—2441no—
340C2×C4—2441no—
341C2×C4—2441no—
342C2×C4—2441no—
343C2×C4—2441no—
344C2×C4—2441no—
345C2×C4—2441no—
346C2×C4—2441no—
347C2×C4—2441no—
348C2×C4—2441no—
349C8—82no—
350C8—4882no—
351C22—21no—
352C22—21no—
353C22—21no—
354C22—21no—
355C22—21no—
356C22—21no—
357C22—22no—
358C22—21no—
359C22—42no—
360C22—42no—
361C22—42no—
362C22—42no—
363C22—41no—
364C22—41no—
365C22—41no—
366C22—41no—
367C22—41no—
368C22—84no—
369C22—81no—
370C22—81no—
371C22—84no—
372C22#1683955112yes—
373C22#1683972811yescharacteristic
374C22C2×#1451969111yescharacteristic
375C22#1683974411yescharacteristic
376C4—41no—
377C4—41no—
378C4—41no—
379C4—41no—
380C4—4881no—
381C4—4881no—
382C4—4881no—
383C4—4881no—
384C2—21no—
385C2—21no—
386C2—22no—
387C2—41no—
388C2—42no—
389C2—81no—
390C2#2144416511yescharacteristic
391C2C2×#1683955111yescharacteristic
392C2#2144746611yescharacteristic
subgroupG/H
centerC22C2×#14519691
commutatorC24×C61C22×C4
FrattiniC2×C22⋊C4C22×D61
FittingC2×C61×#323C2
socleC22×C61C2×#99
prime radicalC25×C61C2×C4
cosocleC2×C22⋊C4×C61C23
hypercenterC2×#323D61
hypocenterC61#11543
LCSG ▷ C24×C61 ▷ C22×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C24 ◁ C22×C22⋊C4 ◁ C2×#323

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
3. #21443768C2semidirect
4. #21443748C2semidirect
219. C61#11543semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
#214500972
#214441462
#214437682
#214437482
C2×C61×#3232
#1154361